Generalized Virial Identities: Radial Constraints for Solitons, Instantons, and Bounces

Fuente: arXiv
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Main Author: Lozano-Mayo, Jonathan
Format: Preprint
Published: 2025
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author Lozano-Mayo, Jonathan
author_facet Lozano-Mayo, Jonathan
contents We derive a continuous family of virial identities for O($n$) symmetric configurations, parameterized by an exponent $α$ that controls the radial weighting. The family provides a systematic decomposition of the global constraint into radially-resolved components, with special $α$ values isolating specific mechanisms. For BPS configurations, where the Bogomolny equations imply pointwise equality between kinetic and potential densities, the virial identity is satisfied for all valid $α$. We verify the formalism analytically for the Fubini-Lipatov instanton, BPS monopole, and BPST instanton. Numerical tests on the Coleman bounce and Nielsen-Olesen vortex illustrate how the $α$-dependence of errors distinguishes core from tail inaccuracies: the vortex shows errors growing at negative $α$ (core), while the bounce shows errors growing at positive $α$ (tail). Applications to the electroweak sphaleron, where the Higgs mass explicitly breaks scale invariance, and the hedgehog Skyrmion illustrate the formalism in systems with multiple competing length scales.
format Preprint
id arxiv_https___arxiv_org_abs_2512_23548
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Generalized Virial Identities: Radial Constraints for Solitons, Instantons, and Bounces
Lozano-Mayo, Jonathan
High Energy Physics - Theory
Pattern Formation and Solitons
We derive a continuous family of virial identities for O($n$) symmetric configurations, parameterized by an exponent $α$ that controls the radial weighting. The family provides a systematic decomposition of the global constraint into radially-resolved components, with special $α$ values isolating specific mechanisms. For BPS configurations, where the Bogomolny equations imply pointwise equality between kinetic and potential densities, the virial identity is satisfied for all valid $α$. We verify the formalism analytically for the Fubini-Lipatov instanton, BPS monopole, and BPST instanton. Numerical tests on the Coleman bounce and Nielsen-Olesen vortex illustrate how the $α$-dependence of errors distinguishes core from tail inaccuracies: the vortex shows errors growing at negative $α$ (core), while the bounce shows errors growing at positive $α$ (tail). Applications to the electroweak sphaleron, where the Higgs mass explicitly breaks scale invariance, and the hedgehog Skyrmion illustrate the formalism in systems with multiple competing length scales.
title Generalized Virial Identities: Radial Constraints for Solitons, Instantons, and Bounces
topic High Energy Physics - Theory
Pattern Formation and Solitons
url https://arxiv.org/abs/2512.23548